The Busy Beaver Function, mentioned in this segment, is really quite amazing; one particularly mind-blowing property is that it grows faster than any computable function!!!

(More correctly, no computable function bounds the busy beaver function; i.e. anything you can actually compute, in any way whatsover, will sooner or later be topped by the Busy Beaver!!) We’re planning to come back to this paradoxical sounding statement in a later segment…

But that was just a way-station on the way to Rayo’s number, which is vastly larger than anything you can easily name: essentially, he calls for the biggest number that takes a googol’s worth of symbols to notate, in any well-defined way, and then tops that!

As we saw last week, Graham’s number only takes, maybe, a hundred symbols to write out, so it is hard to get a handle on what Rayo’s number might be!

Al Downing said,

First, how far does Rayos number surpass a meameamealokkapoowa oompa?. Second, the fact the Rayos number is in the Busy Beaver Function, are there ANY other computable functions which are beyond the Busy Beaver Function?.